A267711 Numbers k such that k mod 3 = k mod 5.

0, 1, 2, 15, 16, 17, 30, 31, 32, 45, 46, 47, 60, 61, 62, 75, 76, 77, 90, 91, 92, 105, 106, 107, 120, 121, 122, 135, 136, 137, 150, 151, 152, 165, 166, 167, 180, 181, 182, 195, 196, 197, 210, 211, 212, 225, 226, 227, 240, 241, 242, 255, 256, 257, 270, 271, 272, 285, 286

Offset

1,3

Comments

Periodic differences between the consecutive terms (1,1,13,1,1,13,1,1,13,1,1...).

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

a(n) = (1/3)*(15*n - 12*cos((2*Pi*n)/3) + 4*sqrt(3)*sin((2*Pi*n)/3) - 27).

G.f.: x^2*(13*x^2+x+1) / ((x-1)^2*(x^2+x+1)).

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4. - Colin Barker, Jan 28 2016

Mathematica

Select[ Range[0, 10000], (Mod[#, 3] == Mod[#, 5]) &]

Prog

(PARI) lista(nn) = for(n=0, nn, if(n%3 == n%5, print1(n, ", "))); \\ Altug Alkan, Jan 19 2016
(PARI) concat(0, Vec(x^2*(1+x+13*x^2)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Jan 28 2016

Crossrefs

Cf. A267540.

Sequence in context: A322149 A163480 A037312 * A108472 A039771 A032934

Adjacent sequences: A267708 A267709 A267710 * A267712 A267713 A267714

Keyword

nonn,easy

Author

Mikk Heidemaa, Jan 19 2016

Status

approved